It is known in the art to employ a fuse circuit that when tripped in an overcurrent condition will terminate supply of current to the load. It is a disadvantage of such a fuse circuit that the protection mode terminates current delivery. Further advances in fuse circuit design provide for an electronic fuse circuit (sometimes referred to in the art as an “e-fuse” circuit) that senses an overcurrent condition and responds thereto by continuing to deliver some current to the load, albeit at a reduced level. Such e-fuse circuits typically have a trip current (Itrip) threshold that must be exceeded before the overcurrent condition is detected. In response to overcurrent detection, the e-fuse circuit will cause the output current level to be reduced to a limited current (Ilim). The gap between the trip current Itrip the limited current Ilim can be undesirably wide. A need accordingly exists in the art for an e-fuse circuit configured for operation with closely related values for Itrip and Ilim.